Qubit-efficient simulation of thermal states with quantum tensor networks

Understand

We present a holographic quantum simulation algorithm to variationally prepare thermal states of $d$-dimensional interacting quantum many-body systems, using only enough hardware qubits to represent a ($d$-1)-dimensional cross-section.

• This technique implements the thermal state by approximately unraveling the quantum matrix-product density operator (qMPDO) into a stochastic mixture of quantum matrix product states (sto-qMPS).
• The parameters of the quantum circuits generating the qMPS and of the probability distribution generating the stochastic mixture are determined through a variational optimization procedure.
• We demonstrate a small-scale proof of principle demonstration of this technique on Quantinuum's trapped-ion quantum processor to simulate thermal properties of correlated spin-chains over a wide temperature range using only a single pair of hardware qubits.